In this work we continue the study of inner (outer) capacities and inner (outer) capacitary measures of sets \(A\subset X\)  for suitable kernels \(\kappa \)  on \(X\) , the main emphasis being placed on the establishment of alternative characterizations of these concepts for arbitrary \(A\) . (In the existing literature on this subject, mainly pertaining to the classical kernels on \(\mathbb {R}^n\) , one usually imposed upon \(A\)  some topological restrictions, see e.g. [1]}, [2]},
[3]}, [4]}, [5]}.)
